Today’s math story problem is a classic problem that is seen in the book:

The King’s Chessboard by David Birch

Similar to *The Lion’s Share*, this classic folktale teaches important lessons on character and the dangers of pride, while also presenting a fascinating mathematical problem.

When a King forces the wise man to choose a reward for his service, the man says he simply wants one grain of rice for the first square on the chessboard, then two for the second square, then four, then eight, etc. doubling until they get to the 64th square. So the question becomes, “Just how much rice is that?” The King, being too proud to look foolish or ask for help with the math, simply grants his request.

While this picture book is intended for young children, you can certainly use this story (and the math problem) with much older students. I have presented this problem to students to solve as an introduction to exponential functions and how they grow, but you could also use this as an example of a geometric series. It’s also a good example of using a zero power or capital sigma notation.

To help you and your students explore this problem, I have created a printable pack with the question and a few discussion questions (and answer key). I would also encourage you to have students try and sketch a graph of what they observe happening (even if they can’t solve the problem).

**{Click HERE to go to my shop and download The Kings Chessboard Problem Pack!}**

In addition, this download includes another, similar problem for students to consider. They are offered a job and given the choice between two different pay options and must determine which is the better choice. Two different formats (with and without tables) are included so you can decide how much support you want to give students (middle school students could definitely solve this question using the tables that are already set up). An answer key is included for this problem as well.

I hope you and your students have fun reading The King’s Chessboard and exploring the wonders of exponential growth!

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Cliff Cyrus says

How big a chessboard would be required to be able to contain the rice in the last square, assuming perfect spheres of short-grained rice?

Bethany says

Interesting question! Another great extension problem to explore! 🙂